On the ‘independence of trials-assumption’ in geometric distribution

In this note, it is shown through an example that the assumption of the independence of Bernoulli trials in the geometric experiment may unexpectedly not be satisfied. The example can serve as a suitable and useful classroom activity for students in introductory probability courses.     

Multifractal scenarios for products of geometric Lévy-based stationary models

We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein–Uhlenbeck processes driven by Lévy motion and their finite and infinite superpositions. We construct the multifractal, such as log-gamma, log-tempered stable, or log-normal tempered stable scenarios.     

On some geometric properties of generalized Orlicz–Lorentz function spaces

In this article we continue investigations concerning generalized Orlicz–Lorentz function spaces _Λφ${\Lambda }_{\phi }$ initiated in the papers (Foralewski, 2011)  and  (cf. also (Foralewski, 2008)  and ). First, it is shown that modular _?φ${?}_{\phi }$ is orthogonally subadditive. Next, monotonicity properties are considered. In order to get sufficient conditions for uniform monotonicity of the space _Λφ${\Lambda }_{\phi }$ a strong condition of _Δ2${\Delta }_2$ type and the notion of regularity of the generated Musielak–Orlicz function φ$\phi$ are introduced. Finally, criteria for non-squareness of _Λφ${\Lambda }_{\phi }$ are presented.     

On ordinary generalized geometric–arithmetic index

The ordinary generalized geometric–arithmetic index of graphs is introduced and some properties especially lower and upper bounds in terms of other graph invariants and topological indices are obtained.     

On the use of simplex methods in constructing quadratic models

In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of function evaluations have been reduced obviously through our algorithms.     

On consistency of stochastic dominance and mean–semideviation models

We analyze relations between two methods frequently used for modeling the choice among uncertain outcomes: stochastic dominance and mean–risk approaches. New necessary conditions for stochastic dominance are developed. These conditions compare values of a certain functional, which contains two components: the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree. If the weight of the semideviation in the composite objective does not exceed the weight of the expected value, maximization of such a functional yields solutions which are efficient in terms of stochastic dominance. The results are illustrated graphically. Received: September 15, 1998 / Accepted: October 1, 2000?Published online December 15, 2000     

On structure of cluster algebras of geometric type Ⅰ:In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.     

On left (right) ρ-transitive geometric spaces

In this article, first we generalize the concept of $\mathfrak{B}$-parts in a geometric space with respect to a binary relation $\rho$ and then we study left (right) $l{\mathfrak{B}}_{\rho }$-closures ($r{\mathfrak{B}}_{\rho }$-closures, respectively). Finally we introduce and investigate the notions left $\rho$-strongly transitive geometric spaces and left $\rho$-emphatic strongly transitive geometric spaces.     

On the geometric analysis of a quartic–quadratic optimization problem under a spherical constraint

Mathematical Programming - This paper considers the problem of solving a special quartic–quadratic optimization problem with a single sphere constraint, namely, finding a global and local...     

On occupation times in the red of Lévy risk models

In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level 0) up to an (independent) exponential horizon for spectrally negative Lévy risk processes and refracted spectrally negative Lévy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum.     

On Infinitesimal Ⅱ—isometry of Surfaces

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On Filters of Double MS—algebras

51.IntroductionThestudyofOckhamalgebraswasinitiatedbyJ-Berman[1j.AnOckhamalgebrasisanalgebra(L;V,A,O,1)oftype(2,2,1,o,o)where(L;V,AlO,1)isadistributivelatticeandfisadualendormorphism;thatis,theequationsf(o)=lf(1)=of(xVY)=f(x)Af(y),f(xAy)=f(x)Vf(x)holdidentically.AnMS-algebraisanOckhama1gebra(LiV,A,', ,o,1)whichsatisfiesthecondition:(aeL)aSa'-AnOckhamalgebrawhichsatifiesthecondictiona2P(a)willbecalledadualMS-algebraandtheunaryoperationdenotedby .AdoubleMS-algebraisanalgebra(L;V,A,…     

Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?

Vernic (2006), Bolancé et al. (2008), and Eling (2012) identify the skew-normal and skew-student as promising models for describing actuarial loss data. In this paper, we change the focus from the liability to the asset side and ask whether these distributions are also useful for analyzing the investment returns of insurance companies. To answer this question, we fit various parametric distributions to capital market data which has been used to describe the investment set of insurance companies. Our results show that the skew-student is an especially promising distribution for modeling asset returns such as those of stocks, bonds, money market instruments, and hedge funds. Combining the results of Vernic (2006), Bolancé et al. (2008), Eling (2012), and this paper, it appears that the skew-student is a promising actuarial tool since it describes both sides of the insurer’s balance sheet reasonably well.     

On the long-time dynamics of nonautonomous predator–prey models with mutual interference

The longtime behaviour of a nonautonomous bidimensional Hassell predator?Cprey model with mutual interference is investigated. The existence of an absorbing set in the phase space is shown, and necessary and sufficient conditions guaranteeing the nonlinear, global, asymptotic stability of the positive solutions have been found by using the Liapunov direct method.